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8.3 Representing Relations. Consider the following relations on A={1,2,3,4}. Consider the matrix M R1 = | 1 1 0 1 | | 0 1 0 0 | | 1 1 1 0 | | 0 1 1 1 | Express as ordered pairs: Which characteristics does R1 have: RSAT?. Express in other formats.

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consider the following relations on a 1 2 3 4
Consider the following relations on A={1,2,3,4}

Consider the matrix MR1= | 1 1 0 1 |

| 0 1 0 0 |

| 1 1 1 0 |

| 0 1 1 1 |

Express as ordered pairs:

Which characteristics does R1 have: RSAT?

express in other formats
Express in other formats

Consider the matrix MR1= | 1 1 0 1 |

| 0 1 0 0 |

| 1 1 1 0 |

| 0 1 1 1 |

Express R1 in the following formats:

  • Graphical
other formats
…other formats

Consider the matrix MR1= | 1 1 0 1 |

| 0 1 0 0 |

| 1 1 1 0 |

| 0 1 1 1 |

  • Digraph (directed graphs)
determine whether the following are rsa
Determine whether the following are RSA:

M R2 = |1 1 1 0 | M R3 = |1 1 1 0 | M R4 = |1 1 0 1 |

|1 1 0 0 | |1 1 0 0 | | 0 1 0 0 |

|0 0 0 1| |1 0 0 0 | |1 0 1 0 |

|1 0 1 1 | |0 0 0 0 | |0 1 0 1 |

R S A R S A R S A

T will be in a later section

find general forms for each property
Find General Forms for Each Property

 Reflexive

Symmetric

Anti-symmetric

challenge
Challenge:
  • Can you find a matrix that is both symmetric and anti-symmetric?

Neither?

matrices m r5 r6 m r5 v m r6
Matrices– MR5R6 = MR5 v MR6

Consider the matrices:

MR5= and MR6=

Find MR R6= MR5 v MR6

find m r5 r6 m r5 m r6
Find MR5∩R6 = MR5 ^ MR6

Consider the matrices:

MR5= and MR6=

Find MR5∩R6 = MR5 ^ MR6

find m r6 r5 m r5 m r6 note order note the boolean symbol has a dot in a circle
Find MR6°R5 = MR5 MR6(note order)note: the Boolean symbol has a dot in a circle

Consider the matrices:

MR5= and MR6=

Find MR6 °R5 = MR5 MR6 (note order)

more ex
More ex

Consider MR1 and MR7= |0 0 0 1|

|0 0 1 0 |

|0 1 0 0 |

|1 0 1 1 |

Find MR1R7

Find MR1∩R7

more ex1
More ex

Consider MR1 and MR7= |0 0 0 1|

|0 0 1 0 |

|0 1 0 0 |

|1 0 1 1 |

Find MR7 ο R1 = MR1 MR7

determine what properties we would see in a digraph that is
Determine what properties we would see in a digraph that is:

 Reflexive

 Symmetric

Anti-symmetric

Transitive